Schedule and Homework
Syllabus

Homework Policy

• You are encouraged to discuss ideas with other students. Nonetheless, every piece of work you turn in must be your own. 
• In each set a selected subset of problems will be graded  and the emphasis will be put on checking
  your thought process and clear exposition  in addition to getting the numerical answers.
  Do NOT assume the grader "knows the stuff, so will understand whatever you jot down", but make an
  effort to write in a way so that your solutions  are easy to follow.
• It is your responsibility to make sure your homework is readable, that you communicate your solutions clearly. If the grader is unable to decipher what you have written, you might end up getting zero points for your homework set. So take care of your work. For example,  state clearly the problem number;write in a logical order as opposed to "all over the place";include comments  (if you make a calculation error, but your approach is correct you  still get partial credit). 
• In addition, in order to be able to handle large volumes of papers and to return your homework within a reasonable time You need to STAPLE! If your homework is not stapled, it will NOT be accepted. 
• I will drop two of the lowest homework grades. So if you have to miss a homework assignment because of an emergency, then it can be dropped as  the  lowest grades.  There is no credit for late homework

This syllabus is meant to be a tentative schedule for the semester.

Week	Topic(s)/Sections Covered	Homework	DueDate /Solution
Aug. 21	Introduction/1.1
Aug. 23	Directional Fields/1.1	Sec 1.1 Do Extra homework (Click on it. You will see the assignment).	Aug 28
Aug. 25	Classification of Differential Equations 1.3	Sec1.3 (p24) 5,  6, 9, 12(In these four problems, just determine the order of the given differential equations.)	Aug 28 Solution to hw1
Aug. 28	Classification of Differential Equations 1.3 Separable equations/1.2, 2.2	Sec1.3 (p24) 5,  6, 9, 12(In these four problems,  determine whether the the  given differential equation is linear or not) Sec1.2 (p15) 1b, 2b (Solve these initiall value problems and describe the behavior of the solution depending on the initial values.)	Sep.  6
Aug. 30	Separable equations 2.2 Quiz	Sec 2.2(p47)  7,  14, 21, 30	Sep.  6
Sep. 1	First-order linear equations/ 2.1	Sec 2.1( p39) 9, 10, (Just find the general solution and determine how solution behaves as t approaches infinity), 14,  31	Sep.  6 Solution to hw2
Sep. 4	Labor Day
Sep   5	Last date to drop
Sep   7	Theorem on existence and uniqueness/2.4, Quiz	Sec 2.4(p75)  1, 4, 5,7, 8, 14, 27,28	Sep   11 Solution to hw3
Sep. 8	Theorem on existence and uniqueness/2.4,
Sep. 11	Autonomous equations/2.5 Quiz	Sec 2.5(p88):7, 9, 10,  13,  21	Sep   20 (due after the first midterm)
Sep.13	Exact equation /2.6	Sec 2.6 (p99)  3, 4,  10, 16	Sep   20 (due after the first midterm) Solution to hw4
Sep. 15	Review  and Catch up!
Sep. 18	First Midterm(in class)
Sep. 20	Second order equation/3.1	Sec 3.1 (p142) 4, 8, 10,  21, 23, 24(Hint for 23 and 24: The solution y=ce^(r1 t) + d e^(r2 t) converges to 0 as t approaches infinity if r1 < 0 and r2 < 0, The solution y=ce^(r1 t) + d e^(r2 t) is unbounded  as t approaches infinity if r1 > 0 and r2>0.)	Sep   25
Sep. 22	Fundamental Solutions; Wronskian; Linear Superposition/3.2	Sec3.2 (p151) 9, 12, 13, 16 (Hint: Compute y(0) and y'(0).),  24, 25	Sep   25 Solution to hw5
Sep. 25	Linear Independence/3.3	Sec3.2 (p151) 25 Sec3.3 (p158) 15, 18, 20, 24	Oct. 2
Sep. 27	Quiz Complex roots & Characteristic equations/3.4	Sec3.4(p164) 9, 11,  18,  27	Oct. 2
Sep. 29	Repeated roots/3.5	Sec3.5(p172)  2, 12,   28, 37	Oct. 2 Solution to hw6
Oct. 2	Reduction of order/3.5 Euler equations /5.5 Method of Undetermined Coefficients/3.6 Quiz	Sec5.5(p278) 1, 3, 4, 14 Sec3.6(p184)  1, 2, 6, 11,	Oct. 9
Oct. 4	Method of Undetermined Coefficients/3.6	Sec3.6(p184)  12, 14, 17	Oct. 9
Oct. 6	Variations of Parameter, 3.7	Sec3.7(190) 3, 5, 6, 14	Oct. 9 Solution to hw7
Oct. 9	Application, 3.9 Quiz
Oct. 11	Review and Catch Up!
Oct. 13	Second Midterm
Oct. 16	Fall Break
Oct. 18	Higher order equation 4.1	Sec 4.1 (p222) 3, 6	Oct. 25
Oct. 20	Higher order homogeneous equation 4.2	Sec 4.2 (p230) 12, 14, 15,  22,  29(Just find the solution. You don't have to plot its graph.)	Oct. 25
Oct. 23	Nonhomogeneous higher order equation 4.3 Quiz	Sec 4.3 (p235) 1, 4, 6, (Use the method ofAnnihilators to do the following problems. You need to show your work.) 13, 15, 17, 18	Oct. 30
Oct. 25	Variation of Parameters, Laplace transform/4.4, 6.1	Sec 6.1  Use table 6.2.1 on page 319 to find the Laplace transform of the following functions. (a) 2t^2 + sin(2t) +e^t cos(2t) (b) t e^(2t) - e^t sin(2t)	Oct. 30
Oct. 27	Laplace transform 6.1 Initial value problem 6.2 Last date to withdraw	Sec 6.2 (p 322) 12, 13, 18	Oct. 30
Oct. 30	Initial value problem 6.2 Quiz
Nov. 1	Initial value problem 6.2	Sec 6.2 (p 322) 21, 22,  23	Nov 6
Nov. 3	Step functions, 6.3 Discontinuous forcing 6.4	Sec 6.3(p330) 7, 8, 9, 10	Nov 6
Nov. 6	Discontinuous forcing 6.4 Quiz	Sec 6.4(p337) 1, 5, 9	Nov 13
Nov. 8	Impulse functions 6.5	Sec 6.5(p344) 2, 3, 11	Nov 13
Nov. 10	Veterans Day!
Nov. 13	Convolutional integral 6.6 Quiz	Sec6.6(p351)7,  9, 11,  13,  14, 19	Nov 20
Nov. 15	Convolutional integral 6.6
Nov. 17	Review and Catch up!
Nov. 20	Midterm III
Nov. 22	Thanksgivings!
Nov. 24	Thanksgivings!
Nov. 27	First Order Linear Equations, 7.4,  7.5	Sec7.5(p398) (Find the solution and Draw the trajectories of the solution and analyze the stability of origin) 1, 5, 6	Dec. 4
Nov. 29	First Order Linear Equations, 7.5
Dec. 1	First Order Linear Equations, 7.6	Sec7.6(p410) Find the solution of the following problems.  1, 2,  3,  9	Dec. 4
Dec. 4	First Order Linear Equations, 7.6 Quiz
Dec 6	Series Solutions of Linear Equations  Ch5
Dec. 8	Series Solutions of Linear Equations  Ch 5
December 13  (Wednesday) 12:30~2:30 p.m.	Final Exam

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